Kardashian As X Factor Host?

Sources connected with the show tell us ... they have whittled down the list of finalists to 6, and Khloe is on it.

We're told Khloe would like the gig, but she's not going to get it without a screen test. Production sources tell us ... producers will be doing screen tests in the next 2 weeks. Our sources say they will NOT buy a pig in a poke, and anyone who wants the hosting job must audition.